State Estimation of Positive Switched Interval Systems with Metzler–Takagi–Sugeno Fuzzy Models

Abstract

This paper addresses the problem of estimating the state of a class of interval and positive nonlinear switched systems. The considered system class is represented by Metzler–Takagi–Sugeno fuzzy switched models with positive Lipschitz nonlinear functions and bounded disturbance. The fuzzy switching interval observers need real-time measurable values of premise variables. The introduced design method in this paper allows us to compute the lower and upper bounds of the system state under assumption that unknown disturbances are norm-bounded, computing the observer gain to achieve such robustness. Formulations and proofs of the design condition for switching fuzzy positive interval observers document that the diagonal stabilisation principle is implementable by a common set of LMIs in the construction of strictly positive interval observer gains, guaranteeing Metzler and Hurwitz observer system matrices and positiveness of the lower and upper bounds of the estimated system states. Design conditions for the interval-switching observer structures are formulated via linear matrix inequalities to also ensure H∞-norm disturbance attenuation and corresponding Lipschitz parameter upper bounds. The proposed algorithm structures are informal and easily creatable as is illustrated by a numerical example.